This was not a performance to have the Napoli scouts trembling, ahead of the Champions League last 16 showdown here on Wednesday night, but for Roberto Di Matteo and everyone connected with Chelsea, the result was everything. After the angst of recent weeks, on and off the field, which culminated in the sacking of André Villas-Boas last Sunday, there was comfort to be located in a narrow victory.

Chelsea's fourth Premier League win in 13 attempts was secured by Didier Drogba's neatly taken goal against a Stoke team that played for 69 minutes with 10 men. Ricardo Fuller's dismissal for an inexcusable stamp on Branislav Ivanovic was foolish in the extreme and it drew condemnation from his manager Tony Pulis.

Di Matteo's team dominated without ever truly quickening the pulse, although they did hit the woodwork three times and create chances, particularly in the first half. The football was formulaic; the tempo and the excitement value low. Chelsea, though, would argue that it was not their fault and that they did everything to force the issue.

Stoke tend to play a certain way on their travels and when they must fight without the full compliment, their backs become pinned even more closely to the wall. Di Matteo noted the difficulty in breaking them down, even before the sending-off.

It always felt as though one goal would prove decisive and it came when the substitute Juan Mata found Drogba with an incisive pass. The Ivorian's first touch looked heavy but his second took him around the Stoke goalkeeper Asmir Begovic. His third brought up his 100th Premier League goal and saw him become the first African player to reach the landmark. The club must surely endeavour to ensure that he does not leave on a free transfer in the summer.

"Sometimes during the season, you have to win like this," Di Matteo said. "It's not always going to be easy or pretty. We scored goals against Bolton, for example, but sometimes you have to win a bit scrappy. It was a big goal for Didier and for the team. His contract is a club matter. Didier has been a tremendous player for this club."

Di Matteo's caretaker charge has started in solid fashion. The victory followed the 2-0 success at Birmingham City in the FA Cup last Tuesday.

"It's two wins, two clean sheets: you gain confidence and belief from that," he said. But he was clear that a more impressive performance would be needed against Napoli to overturn the 3-1 first-leg deficit.

The game was shaped by Fuller's sending-off, although Di Matteo noted that Stoke played with two deep-lying banks of four throughout. Fuller had already tangled with Ivanovic in his own half when he contested a ball with the Serb deep in Chelsea territory.

Ivanovic did raise his leg to make contact with Fuller's shin, after the ball had gone, but Fuller's reaction, aiming a vicious stamp at Ivanovic's nether regions, was disproportionate and gave the referee Andre Marriner no option. The old joke about the player getting the ball did not help to remove the water from Ivanovic's eyes. Nor was it any way for Fuller to mark his first Premier League start since New Year's Day 2011.

"That makes it doubly disappointing," Pulis said. "It was a ridiculous reaction from Ric. He is prone to that. He's a great lad and he was the first to apologise to everyone in the dressing room. But it was unacceptable. We will see whether I fine him. Everything we do will be within the football club."

Chelsea did everything but score in the first-half of a muscular contest and most of the clearest chances fell to Ivanovic. The defender thumped a free header from Frank Lampard's corner over the crossbar; he drew a save from Begovic with a looping header, following more prompting from Lampard and, on 41 minutes, he rattled the bar after Robert Huth's poor clearance.

John Terry, who returned unscathed after his knee operation, also hit the bar, with a header from another Lampard corner while Gary Cahill, preferred to David Luiz at the start, tested Begovic from distance, and Ryan Shawcross almost put through his own goal with a backwards header. For Stoke, Jon Walters had a shot blocked by Cahill in the 17th minute. Mata started on the bench as Di Matteo sought greater physicality – yet the substitutions were positive and Chelsea were on the front foot throughout. Stoke, though, who resemble a team of man-mountains, do not give an easy ride.

Chelsea had been restricted to efforts from distance in the second half, although Drogba's free-kick drew an excellent save from Begovic and there was the sense that they were beginning to labour when they fashioned the breakthrough. The relief was palpable.

Stoke's response was a speculative effort from Andy Wilkinson from the halfway line that was not too far away and a shot from the substitute Cameron Jerome that flashed wide. Mata's curling free-kick from 25 yards hit the post and Daniel Sturridge, also on from the bench, went close.

It was never going to be pretty. Nobody in Chelsea blue could grumble.